Hierarchical Passive Beamforming for Reconfigurable Intelligent Surface Aided Communications

In reconfigurable intelligent surfaces (RISs) aided communications, the existing passive beamforming (PB) design involves polynomial complexity in the number of reflecting elements, and thus is difficult to implement due to a massive number of reflecting elements. To overcome this difficulty, we propose a reflection-angle-based cascaded channel model by adopting the generalized Snell's law, in which the dimension of the variable space involved in optimization is significantly reduced, resulting in a simplified hierarchical passive beamforming (HPB) design. We develop an efficient two-stage HPB algorithm, which exploits the angular domain property of the channel, to maximize the achievable rate of the target user. Simulation results demonstrate the appealing performance and low complexity of the proposed HPB design.